Final answer:
The sum of the interior angles of a polygon with (2n+4) sides, when the sum of the interior angles of an n-sided polygon is known as S, is 2S + 360°.
Step-by-step explanation:
If S is the sum of the interior angles of a regular n-gon, the formula to find S is (n - 2) × 180°. To express the sum of the measures of the interior angles of a polygon with (2n+4) sides using S, we first need to find the relationship between n and 2n+4 side polygon.
The sum of the interior angles for a polygon with 2n+4 sides would be [(2n+4) - 2] × 180°. Simplifying the equation gives us 2n+2 times 180°, which can be further simplified to (2n × 180°) + (2 × 180°). Since we know the sum of interior angles for an n-sided polygon is S, which equals (n - 2) times 180°, we can express 2n × 180° as 2 × S + 360°.
Therefore, the sum of the interior angles of a polygon with (2n+4) sides is 2S + 360°.